Exact solution of N directed non-intersecting walks interacting with one or two boundaries

The partition function for the problem of an arbitrary number of directed non-intersecting walks interacting with one or two walls parallel to the direction of the walks is calculated exactly utilizing a theorem recently proved concerning the Bethe ansatz for the eigenvectors of the transfer matrix of the five-vertex model. This theorem shows that the completeness of the Bethe ansatz eigenvectors for the N-walk transfer matrix can be deduced from the completeness of the one-walk eigenvectors.